To address the challenges associated with DMD, researchers have derived many variations on the original algorithm, including
sparsity promoting DMD [1]},
DMD with control [2]},
noise-robust variants [3]}, [4]}, [5]}, [6]},
recursive DMD [7]},
online DMD [8]}, [9]},
and versions for under-resolved data in space or time [10]}, [11]}, [12]}.
At present, the most widely used variant is `exact DMD' [13]}, which phrases the DMD solution in terms of the Moore–Penrose pseudoinverse.
This solution produces a more even distribution of errors between the terms.
Due to its simplicity and widespread use, most of the comparisons in this paper are made between exact DMD and piDMD.
